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In Boolean algebra, Petrick's method [1] (also known as Petrick function [2] or branch-and-bound method) is a technique described by Stanley R. Petrick (1931–2006) [3] [4] in 1956 [5] [6] for determining all minimum sum-of-products solutions from a prime implicant chart. [7]
The algorithm for solving a problem from a decomposition tree includes two operations: solving a subproblem relative to a node and creating the constraint relative to the shared variables (the separator) between two nodes. Different strategies can be used for these two operations.
The implication graph for the example 2-satisfiability instance shown in this section. A 2-satisfiability problem may be described using a Boolean expression with a special restricted form. It is a conjunction (a Boolean and operation) of clauses, where each clause is a disjunction (a Boolean or operation
Nevertheless, as of 2007, heuristic SAT-algorithms are able to solve problem instances involving tens of thousands of variables and formulas consisting of millions of symbols, [1] which is sufficient for many practical SAT problems from, e.g., artificial intelligence, circuit design, [2] and automatic theorem proving.
In this basic backtracking algorithm, consistency is defined as the satisfaction of all constraints whose variables are all assigned. Several variants of backtracking exist. Backmarking improves the efficiency of checking consistency. Backjumping allows saving part of the search by backtracking "more than one variable" in some cases.
Flowchart of using successive subtractions to find the greatest common divisor of number r and s. In mathematics and computer science, an algorithm (/ ˈ æ l ɡ ə r ɪ ð əm / ⓘ) is a finite sequence of mathematically rigorous instructions, typically used to solve a class of specific problems or to perform a computation. [1]
A node N, labelled by a problem P, is a success node if there is a method of the form P if nothing (i.e., P is a "fact"). The node is a failure node if there is no method for solving P. If all of the children of a node N, conjoined by the same arc, are success nodes, then the node N is also a success node. Otherwise the node is a failure node.
In computer science and formal methods, a SAT solver is a computer program which aims to solve the Boolean satisfiability problem.On input a formula over Boolean variables, such as "(x or y) and (x or not y)", a SAT solver outputs whether the formula is satisfiable, meaning that there are possible values of x and y which make the formula true, or unsatisfiable, meaning that there are no such ...